Gaming computer for $800

Budget : $850
Resolution : Pref 1920 x 1080, will go lower if needed
Games : Mainly used for WOW/Starcraft/League of Legends/Skyrim
Any other intensive software or special things you do (Frequent video encoding, 3D modeling, etc) : No
Country : Australia (Western Australia to be precise)
Parts that can be reused: No
Do you need an OS? Yes, pref no windows 8
Do you need peripherals (e.g. monitor, mouse, keyboard, speakers, etc)? Keyboard and Monitor needed

I had this as a starting list for a computer build for a friend, but having issues with getting it to around $850